Microscopic inclusion statistics in a discrete 1-body spectrum

We present the microscopic formulation of inclusion statistics, a counterpoint to exclusion statistics in which particles tend to coalesce more than ordinary bosons. We derive the microscopic occupation multiplicities of 1-body quantum states and show that they factorize into a product of clusters of neighbouring occupied states with enhanced statistical weights. Applying this statistics to a one-dimensional gas of particles in a harmonic well leads to a Calogero-like n-body inclusion spectrum with interesting physical properties.